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In Physics , an inverse-square law is any Physical Law stating that some physical Quantity or strength is Inverse ly Proportional to the Square of the Distance from the source of that physical quantity.

For an Irrotational Vector Field the law corresponds to the property that the Divergence is zero outside the source.

In particular the inverse square law applies in the following cases:

  • The Gravitational attraction between two massive objects, in addition to being directly proportional to the product of their masses, is inversely proportional to the square of the distance between them; this Law was first suggested by Ismael Bullialdus but put on a firm basis by Isaac Newton ;


  • The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is Coulomb's Law ;


  • The Intensity of Light radiating from a Point Source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source. An object (of the same size) twice as far away, receives only 1/4 the Energy (in the same time period). More generally, the Irradiance , i.e., the Intensity (or Power per unit area in the direction of Propagation ), of a Spherical Wavefront varies inversely with the square of the distance from the source (assuming there are no losses caused by Absorption or Scattering ). For example, the intensity of radiation from the Sun is 9140 Watt s per square meter at the distance of Mercury (0.387AU); but only 1370 watts per square meter at the distance of Earth (1AU)—a three-fold increase in distance results in a nine-fold decrease in intensity of radiation.



:For another example, let the total power radiated from a point source, e.g., an omnidirectional Isotropic Antenna , be P \ . At large distances from the source (compared to the size of the source), this power is distributed over larger and larger spherical surfaces as the distance from the source increases. Since the surface area of a sphere of radius r \ is A = 4 \pi r^2 \ , then Intensity ''I'' of radiation at distance ''r'' is

:: I = rac{P}{A} = rac{P}{4 \pi r^2}.

:: I \propto rac{1}{r^2}